(a) A shear parallel to the x-axis with (0, 1) (3, 1) Multiple Transformations Give the transformation matrix for each of the following transformations. More Transformations For each of the following matrices, draw a diagram to show their effects on the unit square and describe (as best you can) the transformation(s) which they represent. (e) Find the determinant of the transformation matrix.ģ. (d) By considering the areas of the square OPQR (O is the origin) and the rectangle OP’Q’R’, what should the determinant of the matrix be? (b) Describe the main features of the transformation, saying particularly how it differs from an enlargement by a simple dilation. Two-Way Stretch The quadrilateral PQRS with coordinates P (1, 0), Q (1, 1), R (0, 1), and S ( 1, 1) is mapped to P’Q’R’S’ where P ' (3, 0), Q ' (3, 2), R ' (0, 2), and S' ( 3, 2) (a) Sketch this transformation of the quadrilateral PQRS (d) Does the area change? What is the determinant of the transformation matrix?Ģ. (c) Describe the transformation in words. Shearing Transformation Consider the unit square with vertices A (0, 0), B (1, 0), C (1, 1), D (0, 1) mapped to the parallelogram A'B'C'D' where A ' (0, 0), B' (1, 0), C ' (3, 1), and D ' (2, 1) (a) Draw the object and image. Name _ Worksheet 11.2 Transformations II Due Mon March 2nd 1.
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